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 A358445 Euler's 4 X 4 magic square of squares. 2

%I #52 Feb 12 2024 08:39:21

%S 4624,841,1681,1369,289,961,6241,1024,3481,784,529,3721,121,5929,64,

%T 2401

%N Euler's 4 X 4 magic square of squares.

%C This is the first known magic square of squares; Euler sent it to Lagrange in 1770.

%C The magic sum is 8515.

%H Paul Pierrat, François Thiriet, and Paul Zimmermann, <a href="https://web.archive.org/web/20210921105123/https://members.loria.fr/PZimmermann/papers/squares.pdf">Magic Squares of Squares</a>.

%H Philippe Michaud-Rodgers, <a href="https://warwick.ac.uk/fac/sci/maths/people/staff/michaud/magisquarestalk.pdf">Magic Squares of Squares</a>.

%H Ivars Peterson, <a href="https://www.sciencenews.org/article/magic-squares-squares">Magic Squares of Squares</a>.

%e The magic square is:

%e [ 4624 841 1681 1369 ]

%e [ 289 961 6241 1024 ]

%e [ 3481 784 529 3721 ]

%e [ 121 5929 64 2401 ]

%e Equivalently:

%e [ 68^2 29^2 41^2 37^2 ]

%e [ 17^2 31^2 79^2 32^2 ]

%e [ 59^2 28^2 23^2 61^2 ]

%e [ 11^2 77^2 8^2 49^2 ]

%Y Cf. A271580: magic sums of 4 X 4 magic squares composed of squares.

%K nonn,fini,full

%O 1,1

%A _Robert C. Lyons_, Dec 30 2022

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Last modified September 7 07:38 EDT 2024. Contains 375729 sequences. (Running on oeis4.)